Johnson's figure of merit

Johnson's figure of merit is a measure of suitability of a semiconductor material for high frequency power transistor applications and requirements. More specifically, it is the product of the charge carrier saturation velocity in the material and the electric breakdown field under same conditions, first proposed by Edward O. Johnson of RCA in 1965. ^[1]

Note that this figure of merit (FoM), sometimes referred to as JFoM, is applicable to both field-effect transistors (FETs), and with proper interpretation of the parameters, also to bipolar junction transistors (BJTs).

JFoM is meant to identify the relative suitability of a bulk semiconductor material for high power and high speed applications. There are variations on this FoM for evaluating relative merit specifically at high frequencies by including the cut-off frequency of a transistor made of the specific material ^[2] . There are FoMs used for particular power applications like switching for example ^{[3] [4]} .

Example materials

Note that both saturation velocity and breakdown voltage are temperature and doping/impurity level dependent ^{[5] [6]}

Material	Saturation velocity × 105 m/s	Vbreakdown MV/cm	JFoM Si: 1.0	Notes/refs
Silicon	1.0	0.3	1.0	[6] [7] [8]
GaAs	1.2	0.3	1.2	[6] [9] [10]
SiC	2.0	2.5	16.7	[6] [11] [12]
InP	0.67	0.5	1.2	[6] [13] [14]
GaN	2	3	20	[6] [15] [16] [17] [18]
Diamond	2.1	10	70	[19]

JFoM figures may vary significantly between different sources mainly due to temperature effects and sensitivity to material purity and other conditions such as crystal orientation and the measurement technique used. Breakdown field also shows some dependency on the field value itself, and somewhat to the frequency of the field also if it is not a static one. For this reason, high field electron velocities should be used for this estimation. Also, note that semiconductors GaAs and InP, belonging to two-valley family of Group III-V materials ^[20] , have peak electron velocities greater than the high field saturation velocities used here.

External links

• Gallium Nitride as an Electromechanical Material. R-Z. IEEE 2014 Table IV (p. 5) lists JFM (relative to Si) : Si: 1, GaAs: 2.7, SiC: 20, InP: 0.33, GaN: 27.5, also shows V_sat and E_breakdown.

References

1. "Physical limitations on frequency and power parameters of transistors", RCA Review, vol. 26, pp. 163–177, June 1965.
2. "Gallium Nitride: Analysis of Physical Properties and Performance in High-Frequency Power Electronic Circuits", D. K. Saini, Engineering, Materials Science 2015
3. "Power Semiconductor Device Figure of Merit for High-Power-Density Converter Design Applications", H. Wang, F. Wang, Ju. Zhang, Engineering, Physics IEEE Transactions on Electron Devices 2008
4. "Power Semiconductor Devices for Variable-Frequency Drives", B. Baliga, Engineering, Physics Proceedings of the IEEE, 1994
5. Crowell, C. R. and S. M. Sze, Appl. Phys. Lett. 9, 6 (1966) 242-244.
6. .Gallium Nitride as an Electromechanical Material. R-Z. IEEE 2014 Table IV (p 5)
7. Sze, S. M., Physics of Semiconductor Devices, John Wiley and Sons, N.Y., 1981.
8. Hard Switching Characteristics of SiC and GaN Devices for Future Electric Vehicle Charging Stations January 2021MATEC Web of Conferences 335:02007 DOI:10.1051/matecconf/202133502007
9. Blakemore, J.S.,J.Appl.Phys.53, 10 (1982) R123-R181.
10. Kyuregyan, A. S. and S. N. Yurkov, Sov. Phys. Semicond. 23, 10 (1989) 1126-1132.
11. Mickevicius, R., J.H. Zhao, Monte Carlo Study of Electron Transport in SiC. J. Appl. Phys. 83, 6 (1998), 3161-3167.
12. Khan, I. A., J. A. Cooper, Jr., "Measurement of High-Field Electron Transport in Silicon Carbide," IEEE Trans. on Electron Devices, 47, 269 (2000).
13. Windhorn, T. H., L. W. Cook, M. A. Haase, and G. E. Stillman, Appl.Phys. Lett. 42, 8 (1983) 725-727.
14. Kyuregyan, A. S. and S. N. Yurkov, Sov. Phys. Semicond. 23, 10 (1989) 1126-1132.
15. Hard Switching Characteristics of SiC and GaN Devices for Future Electric Vehicle Charging Stations, January 2021MATEC Web of Conferences 335:02007, DOI:10.1051/matecconf/202133502007
16. Albrecht, J.D., R.P. Wang, P.P. Ruden, M. Farahmand, K.F. Brennan, J. Appl. Phys. 83(9) (1998), 4777-4781.
17. K.Boomer, Leif Scheick, Ahmad Hammoud, "Body of Knowledge for GaN Power Electronics", NASA NEPP Program, Office of Safety and Mission Assurance, November 9, 2020
18. NEPAG EEE Parts Bulletin (2012). Gallium Nitride-Worth the Hype, vol. 4, issue 2, pp.1-2
19. J.E. Field, The Properties of Natural and Synthetic Diamond, (Academic Press, London, 1992)
20. P. N. Butcher and W. Fawcett, "The intervalley transfer mechanism of negative resistivity in bulk semiconductors", Proc. Phys. Soc., vol. 86, pp. 1205-1218, 1965.